Simulated Data From a Known Covariance Matrix of Advanced Placement Course Data

Propensity score analysis is widely used for simulating random assignment in observational studies where true random assignment is not possible. In propensity score modeling, a number of covariates are used to estimate the probability that an individual will belong to one of two groups. Prospective participants are then matched on their probabilities of belonging to the two groups rather than on the exact set of covariate values (as in traditional matching methods). However, traditional propensity score analysis can only be used in studies with two groups, such as an experimental and control group. In this study a new method is introduced called piecewise propensity score analysis (PPSA) for ordinal polytomous grouping variables. PPSA was compared with another method of conducting propensity score analysis with ordered categories, marginal mean weighting through stratification (MMW-S) in a 3 x 5 x 4 study across three model misspecification conditions, five matching methods, and four sample sizes (1000, 5000, 10000, 21753). No significant difference were found between PPSA and MMW-S methods across conditions. Linear regression, simple mean difference, or propensity stratification methods are recommended for simulating causal inference.